Limits & Continuity: Let f:Rto R be a positive increasing function with… | AIEEE 2010 | Yukti Vault

Yukti Vault

AIEEE 2010 (Offline)Question 1

Let $f:R\to R$ be a positive increasing function with $\lim_{x\to\infty}\frac{f(3x)}{f(x)}=1$. Then $\lim_{x\to\infty}\frac{f(2x)}{f(x)}=$

Limits & Continuity

$\frac23$$\frac32$$3$$1$✓ Correct answer

Solution

$f$ increasing and positive gives $1\le\frac{f(2x)}{f(x)}\le\frac{f(3x)}{f(x)}\to1$, so the limit is $1$.

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